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If all the politicians on you ballot corrupt, you can rank the lottery option higher than the politicians on your ballot. The net ranking is determined by summing the ballot option relations. You fill seats starting at the top ranked and work your way down, but any candidate equal to or less than the lottery option is tossed. If there are remaining seats, the a citizen lottery is held. There's no opt-in. We pick a random citizen, ask if they'll do the job. They can reject, and we re-roll the lottery until it's filled.

You lose the technical expertise of politicians if you choose this option, but it's extremely good for preventing political entrenchment. You also tend to get people who care deeply about their community accepting the job. Some people claim you'll end up with uneducated people (especially in the short term), but that's both kinda classist and fails to question: what system lead to "so many" uneducated people in the first places? There will also be people who put the lottery option first out of principle. This is good because it means politicians have to have even wider appeal to beat the lottery option (i.e. 70% approve, but 10% those put lottery first out of principle, so only 63% rank them above lottery, beats lottery -- 55% approval with 10% above lottery-firsters puts them at 49.5% above lottery, 50.5% below lottery, so lose to lottery).

It's basically a populous anti-corruption mechanism.